. Author manuscript; available in PMC: 2014 Dec 24.

Published in final edited form as: Psychol Assess. 2011 Sep 12;24(1):173–186. doi: 10.1037/a0025265

Table 4.

Model Fit in the Analysis Sample (N = 3,000)

χ_{S - B}^{2}

Δ χ_{S - B}^{2}

Δdf

Δ^{CI} χ_{S - B}^{2}

Δ^CI df

CFI

RMSEA

Model E

2514.30^*

231

0.614

—

0.976

0.057

Model E^*

380.52^* to 621.79^*

231

0.587 to 0.697

—

0.956 to 0.983

0.058 to 0.072

Model CI

5255.58^*

2310

0.620

—

0.972

0.065

Model WMI

5461.70^*

2526

0.686

350.80^*

216

—

0.972

0.062

Model SMI

5653.54^*

2697

0.688

199.17^*

171

577.00^*

387

0.972

0.060

Model CMI

5921.79^*

2913

0.750

361.98^*

216

947.81^*

603

0.971

0.059

Model CMIr

5963.75^*

2967

0.751

46.50

1007.20^*

657

0.971

0.058

Model CMIrv

5966.26^*

3012

0.794

71.21^*

1082.09^*

702

0.972

0.057

Model CMIrvc

5908.13^*

3102

0.938

147.22^*

1224.00^*

792

0.973

0.055

Model CMIrvcm

6247.31^*

3147

0.972

269.97^*

1447.89^*

837

0.970

0.057

Note. $χ_{S - B}^{2}$ = Satorra-Bentler adjusted chi-square, df = degrees of freedom, SC = scaling correction factor, $Δ χ_{S - B}^{2}$ = Satorra-Bentler adjusted chi-square difference, Δdf = degrees of freedom difference, $Δ^{CI} χ_{S - B}^{2}$ = Satorra-Bentler adjusted chi-square difference to Model CI, CFI = comparative fit index, RMSEA = root mean square error of approximation; Model E: see Table 2; Model E^* = Model E modelled separately in each age group. Given is the range of fit indexes; Model CI = multiple-groups model of configural invariance; Model WMI = multiple-groups model of weak measurement invariance; Model SMI = multiple-groups model of strong measurement invariance; Model CMI = multiple-groups model of strict or complete measurement invariance; Model CMIr = Model CMI plus equal residual covariances, Model CMIrv = Model CMIr plus equal factor variances; Model CMIrvc = Model CMIrv plus equal factor covariances. Model CMIrvcm = Model CMIrvc plus equal factor means.

p < .01.